[{"content":" The ideas in this article have been formalized (including derivations of all knockdown factors) in an AIAA paper and a reference implementation of all the methods has been made available as a MATLAB package called bat-perf.\nBattery Knockdown Factors for Conceptual Design R. A. McDonaldAIAA Aviation 2024Develops and quantifies battery knockdown factors — the gap between cell-level energy density and what is actually usable at the pack level in conceptual design. Provides practical sizing multipliers accounting for thermal management, depth of discharge limits, and aging. Rob McDonald\nSan Luis Obispo, CA\nJanuary 2023\nOriginally published as a series of seven weekly LinkedIn articles from September 7 to October 18, 2022.\nIn Part 1, we identified some differences in the behavior of liquid fuels and batteries that are relevant for the conceptual design of aircraft. In my experience, many would-be electric aircraft developers do not adequately understand these differences.\nIn Part 2, we observed that the cell discharge rate map provides convincing evidence of at least two of our critical differences - that the energy delivered by a cell depends both on the state of discharge and the rate of discharge.\nIn Part 3, we introduced the cell specific energy knockdown factor and also a simple cell performance model appropriate for aircraft conceptual design and performance analysis.\nIn Part 4, we introduced an absolute energy reference for developing the knockdown factors. We also observed that the power a cell can deliver is limited along with other aspects of cell behavior including degradation through use and some aspects of charging.\nIn Part 5, we established reasons to limit the usable charge range of a cell. We also introduced a representative eVTOL mission profile to be used as an example for the rest of the series. We finished by calculating the partial discharge knockdown factor.\nIn Part 6, we developed two more components of the knockdown factor; one for capacity fade and another for finite discharge rate and resistance growth. We also defined the C rate and E rate for a cell.\nIn Part 7, we present the last two components of the knockdown factor and we bring it all together into a single measure of installed battery specific energy.\nPart 1. How Well Do You Know Batteries? It is natural for aircraft designers to try to think about batteries in the same terms as they would liquid fuel. There are tremendous differences, but contrasting them with something familiar gives us a framework for understanding.\nWhile many of these differences receive lip service, I find that many would-be electric aircraft developers don\u0026rsquo;t really understand them. Ask yourself:\nDo you?\nCan you quantify all of these effects?\nDid your quantitative understanding influence your conceptual design trades?\nEnergy Storage Fuel is first and foremost a means for storing energy, so we\u0026rsquo;ll start by comparing fuel and batteries on that basis.\nLiquid fuel: Every pound of fuel is equally energetic.\nThe rate of consumption does not diminish the energy in fuel.\nA fuel tank’s capacity does not diminish with use.\nEnergy required determines the required fuel quantity.\nEvery pound of fuel can be replaced at the same rate.\nBatteries: The energy contained in different parts of a cell are not equal.\nWhen discharged rapidly, a cell will deliver less energy.\nThe capacity of cells degrades with use and time.\nEnergy required may determine the required battery size.\nCharge rate varies – cells are very slow to top off.\nPower Source Though seldom a concern, the fuel flow rate is a means of providing power.\nLiquid fuel: Every pound of fuel is equally powerful.\nFuel can be consumed at almost any rate.\nThe power capability of fuel does not diminish with use.\nPower requirements determine the size of the engine.\nFuel burning A/C perform better at end of mission.\nBatteries: The power available from different parts of a cell are not equal.\nCells can only discharge at a limited rate.\nThe power capability of cells degrades with use and time.\nPower requirements size the motor \u0026amp; drive – and may size the battery.\nBattery powered A/C perform worse at end of mission.\nSo what do you think? I\u0026rsquo;ve been thinking about writing a series of posts to dive into this. Thoughts?\nA) You aren\u0026rsquo;t a professor anymore, don\u0026rsquo;t lecture us on batteries.\nB) BatteryStartup says they will get 800 Wh/kg next year. That is all I need to know.\nC) I\u0026rsquo;m battery curious - tell me more.\nPart 2. Beginnings Before we can discuss, understand, and quantify the differences between batteries and liquid fuel, we need to cover some background, define some terms, and maybe even show an equation or two. Things may start basic, slow, and long - but should pick up as we go along.\nA cell discharge rate map is the fundamental chart depicting cell performance. They are commonly depicted on a manufacturer’s data sheet.\nA rate map depicts the discharge voltage (vertical axis) as a function of cell capacity (horizontal axis) for different constant current discharges (each colored line).\nCell capacity is measured in charge. Here, mAh (milli-Ampere-hours), but you should be familiar with Ah, As, and Coulomb (C) – one C = 1As.\nA meander: You may think it would be more natural to conceptualize cell capacity in terms of energy. Unfortunately, this doesn’t work out. Like mass, momentum, and energy, charge is a conserved quantity. We can track the flow of charge in and out of a cell – the EE’s call this ‘Coulomb counting’.\nYou’ll be glad to know the first law still applies – energy is conserved when charging or discharging a battery. However, some energy goes to waste heat due to the cell’s internal resistance. This ‘lost’ energy would make tracking the contents of a battery very difficult.\nOf course, we do not track the contents of fuel tanks in terms of energy either. Instead we use mass/weight or perhaps volume.\nThe commonly used units of charge (Ah) is admittedly awkward, but analogous to using light-years to measure distance. One Ampere of current is one Coulomb per second flow of charge.\nThe cell depicted in our rate map is nominally a 4200 mAh cell. The horizontal axis depicts the capacity discharged from full such that the cell is full on the left and empty at the right.\nAt a given state of discharge (say 1000 mAh) and discharge rate (say 10 A), the voltage across the terminals will be about 3.8V. Increasing the discharge rate will cause the voltage to drop. Likewise, discharging at the same rate, but at a deeper state of discharge will also occur at a lower voltage.\nThe area under a discharge curve is the energy delivered during that discharge. This is depicted for a full-depth discharge at 10 A as the shaded region below.\nIn order to zoom in on the interesting part of the chart, the vertical axis of discharge rate maps usually does not go to zero, so be careful about visually comparing areas under the curves - there is often more area off the chart than on.\nWe can now see that a 10A discharge of 500 mAh from a relatively full cell will provide more energy than the same discharge from a relatively empty cell.\nPutting this in terms of liquid fuel (without proof or further discussion), we realize that the first pound of fuel in a tank contains the same energy as the last pound of fuel in the tank.\nWe are ready to observe the first of our key differences between liquid fuel and batteries.\nThe energy contained in different parts of a cell are not equal. We can also see that a 1500 mAh discharge starting at the same depth of discharge will provide more energy if performed at a lower discharge rate (say 10A vs. 30A) (the \u0026rsquo;lost\u0026rsquo; energy goes to waste heat due to the cell\u0026rsquo;s internal resistance). The higher rate discharge will also take 1/3 the time.\nIn terms of liquid fuel, we understand that a pound of fuel contains the same energy no matter how quickly we pump it through the lines.\nWe now observe the second of our key differences between liquid fuel and batteries.\nWhen discharged rapidly, a cell will deliver less energy. The discharge rate map has more secrets to reveal, but that is enough to get us started. Become comfortable with rate maps - they\u0026rsquo;ll be back.\nHow am I doing? Thanks to everyone who reacted to my first post - while perhaps smaller in number than hoped, the reaction was entirely positive. So begins the journey.\nPlease let me know how I\u0026rsquo;m doing.\nPart 3. Bottom Line This is one of those stories that requires a lot of background. Here we\u0026rsquo;ll make one more big push to get us ready for the main event.\nUndoubtedly, the critical technology metric for the application of batteries to aircraft primary propulsion is the specific energy - the energy per mass of a battery.\n(Without any offense to power, we will briefly focus our discussion on matters of energy. Don\u0026rsquo;t worry, power\u0026rsquo;s critical role in this story will come.)\nManufacturer\u0026rsquo;s Cell Specific Energy Cell manufacturers quote the cell specific energy under defined idealized laboratory conditions - the energy provided by a cell when discharged in a particular way divided by the cell mass.\n$$e_{\\mathrm{mfg}}=\\frac{E_{S,c}}{m_{c}}$$The manufacturer\u0026rsquo;s cell rated energy is typically obtained from a full-depth discharge at constant current. For \u0026rsquo;energy cells\u0026rsquo; this discharge is relatively slow (say 0.2C), and for \u0026lsquo;power cells\u0026rsquo;, this discharge is substantially faster (say 1C).\nEffective Battery Specific Energy As previously discussed, the energy delivered by a battery depends on both the state of discharge (when the discharge occurs) and the rate of discharge (how the discharge occurs). I.e. the energy delivered depends on the details of the cell discharge profile.\nWe will define the effective specific energy of a battery in the terms most relevant to aircraft design - the energy required for an aircraft to fly the critical sizing mission divided by the mass of the battery pack.\n$$e=\\frac{E}{m_{b}}$$Knockdown Factor We will define a cell energy knockdown factor to account for the differences between the manufacturer\u0026rsquo;s specific energy and the effective specific energy.\n$$e=k\\,e_{\\text{mfg}}$$Much of our coming discussion will focus on understanding and quantifying this knockdown factor for each of the identified differences between liquid fuels and batteries. Spoiler alert - stark realities await.\nModeling a Cell\u0026rsquo;s Behavior A cell\u0026rsquo;s performance can be modeled with a simple equivalent circuit consisting of a voltage source and a resistor in series.\nThe potential across the voltage source is the cell\u0026rsquo;s open circuit voltage and the resistance is the cell\u0026rsquo;s internal resistance. Both the $OCV$ and the $R_i$ are functions of the cell depth of discharge - they depend on where you are in a cell\u0026rsquo;s discharge.\n(Note that here we use the depth of discharge ($x$) as a fraction of the rated cell capacity ($Q$).)\nWe will require $OCV$ and $R_i$ curves like those shown above. These may be provided by the cell manufacturer or they can be reverse engineered from a typical discharge rate map. Although there are theoretical means of predicting these curves, they are almost always empirically derived in practice. The functional form of these curves is irrelevant to our purposes, linear interpolation or functional fits to data are acceptable.\nThe equation for the cell terminal voltage allows us to calculate the cell voltage given the depth of discharge and the rate of discharge. This provides us with an equation of state for the cell.\n$$V\\left(x,I\\right)=OCV\\left(x\\right)-R_{i}\\left(x\\right)\\,I$$(Many cell modeling resources will expend great effort including capacitance in the form of one or more RC circuits in the cell model. This adds an additional time response to the cell\u0026rsquo;s behavior. Fortunately, for purposes of conceptual aircraft design, we can limit ourselves to the cell\u0026rsquo;s steady state resistance. During conceptual design, an aircraft\u0026rsquo;s power draw is typically treated as a series of constant power segments. The time spent at each power level is long compared to the time response of the cell.)\nIn addition to predicting the cell\u0026rsquo;s terminal voltage at any instant in time, we need to track how the cell\u0026rsquo;s state of charge changes with time. For this, we write a simple statement for the conservation of charge.\n$$\\frac{\\mathrm{d}x}{\\mathrm{d}t}=\\frac{I}{Q}$$Given these equations and models, a little bit of algebraic manipulation and some integration is all that we will need to model cell behavior for aircraft design.\n(When the time comes, we will slightly modify these models to account for cell ageing.)\nChecking In If you made it this far, make a comment and let me know what you think.\nAlthough I initially promised a \u0026lsquo;deep dive\u0026rsquo;, I still feel the need to keep these articles pretty high level. Consequently, I don\u0026rsquo;t plan on actually showing the algebraic manipulations of the terminal voltage equation or the integration of the conservation of charge. I\u0026rsquo;m going to trust that if you are sufficiently motivated, you can figure that out. Reach out if more detail is required.\nPart 4. An Absolute Reference The cell specific energy knockdown factor introduced in Part 3 relates the manufacturer\u0026rsquo;s rated specific energy to the effective specific energy for an aircraft. While this is the \u0026lsquo;right\u0026rsquo; metric (most useful to an aircraft designer), it would prove cumbersome to calculate directly.\nInstead, we consider the limit of the energy discharged from a cell as the rate approaches zero. Such a zero current discharge would take infinite time, but it would also suffer no losses to internal resistance. We often think of lossless, infinite-time processes as reversible - we will use that term here.\nThe reversible cell energy is the true energy stored in the cell. When discharged at a finite rate, some of that energy is released as useful electricity and the rest is lost as waste heat.\nJust as the energy for a given discharge is the area under the voltage vs capacity curve, the cell reversible energy is the area under the $OCV$ curve.\nPower is Limited The instantaneous power discharged from a cell may be computed by multiplying the terminal voltage equation by the discharge current.\n$$P\\left(x,I\\right)=OCV\\left(x\\right)\\,I-R_{i}\\left(x\\right)\\,I^{2}$$The maximum power a cell can discharge can be found through the familiar calculus routine. 1) Take the derivative of the power equation with respect to current. 2) Set that equal to zero. 3) Solve for the current at maximum power. 4) Substitute back into the power equation to determine the maximum discharge power given here.\n$$P_{max}\\left(x\\right)=\\frac{\\left(OCV\\left(x\\right)\\right)^{2}}{4\\,R_{i}\\left(x\\right)}$$This power level itself is not particularly useful - it is unreasonably high and other bad things will likely happen before reaching it. In particular, at this power the cell instantaneous efficiency is 50% - half of the cell\u0026rsquo;s energy is going to waste heat.\nThe first important observation is that a limit on power exists - demonstrating another one of our bullets from Part 1: Cells can only discharge at a limited rate.\nThe second important observation is that this power limit is a function of the depth of discharge - another bullet: The power available from different parts of a cell are not equal.\nThe third important observation is that the internal resistance of a cell is intimately linked to the maximum discharge power. Double the internal resistance and the maximum power is cut in half!\nSimilar procedures may be carried out to determine other limits on the cell discharge power. The figure below compares four possible limits on cell power discharge. The magnitudes of these limits are not important - the constraining quantity has been chosen to bring each corresponding power limit to roughly the same value for comparison. The absolute power limit derived above is the solid line on this graph.\nYears ago in EE lab, I learned that everything is a fuse if you put enough current across it. There will be a maximum current limit associated with the cell and the pack. Perhaps it will be determined by the fuseable link connecting each cell. Perhaps it will be determined by a module or pack fuse. Perhaps it will be determined by the gauge of wire connecting the pack to the bus bars - or the dimensions of the bus bar itself. There will be a current limit. It will be shaped like the dashed line in the figure above.\nSimilarly, there will be a minimum voltage limit somewhere in the system. Perhaps it will be determined by the cell cutoff voltage. Perhaps it will be determined by a power electronics brownout condition where it becomes impossible to command full RPM. A cell minimum voltage limit will look like the dotted line in the figure above.\nThere may be other limits. Perhaps a maximum waste heat limit imposed by the battery pack cooling system. A waste heat limit will look like the dash-dot line in the figure above.\nWe again observe that each of these power limits is a function of the depth of discharge of the cell. In particular, we observe that the power limits tend to decrease with depth of discharge. I.e. the battery\u0026rsquo;s limit discharge power is less at the end of a mission than at the start - another bullet from Part 1: Battery powered A/C perform worse at end of mission.\nA battery pack for an aircraft with a large power requirement at the end of the mission will likely be sized by power instead of energy - one more bullet: Power requirements may size the battery.\nThe most common example of such a requirement is an eVTOL vehicle landing at the end of the mission. However, eCTOL vehicles executing a go-around at the end of a mission may also provide a sizing power requirement.\nWe do not have scope to demonstrate it, but like the absolute power limit, each of the power limits discussed here is strongly linked to cell internal resistance. Increasing internal resistance will reduce the maximum power capability of a cell or pack.\nFinally, we observe that these lines are not parallel; depending on the details of the values of each constraint, these lines can and will cross. I.e. which factor is limiting will change throughout the discharge.\nYou may think you can design a power system such that only one power limit is ever active. Or such that no power limit is ever critical. Such a system will never be optimal; it is guaranteed to carry extra mass to provide that margin.\nCell Ageing Cell performance degrades. Anyone who has worked with an old laptop or cell phone has experienced this. Cell degradation is caused by tiny amounts of damage done to the cell. This damage occurs every time we charge or discharge a cell. It can even occur if we just leave a cell sitting on a shelf.\nThere are two primary aspects of cell degradation. The cell capacity will reduce; this is called capacity fade. At the same time, the cell internal resistance will increase; this is called resistance growth or power fade (recall the importance of resistance to power).\nThus we have two more Part 1 bullets: The capacity of cells degrades with use and time. \u0026amp; The power capability of cells degrades with use and time.\nThere are two main sources of cell degradation. Calendar ageing is damage done to a cell over long periods of time independent of charging and discharging. Calendar ageing is most rapid in a cell that is kept fully charged at all times. We are typically less concerned with calendar ageing for aircraft that we hope to operate at high tempo.\nCycling ageing is damage done to a cell during any charge or discharge. The rate of cycling damage depends on the rate of charge or discharge and also on which portion of a cell is cycled.\nIn the data below, we observe that capacity fade and resistance growth are greatest for the cells cycled at the top of charge (gold and purple) and the bottom of charge (blue). The least damage occurs for the cells cycled in the middle of the discharge range (green, red, and cyan).\nJ. Schmalstieg, S. Käbitz, M. Ecker and D. U. Sauer, \u0026lsquo;From accelerated aging tests to a lifetime prediction model: Analyzing lithium-ion batteries,\u0026rsquo; 2013 World Electric Vehicle Symposium and Exhibition (EVS27), 2013\nTheoretically, an aircraft whose battery is sized without consideration of ageing will only be able to execute its design mission once. During that singular mission, some damage to the cell will occur - reducing the capacity and increasing the internal resistance - reducing the range or endurance of the aircraft and its peak power capability.\nAny aircraft destined for practical operation must consider ageing in the pack design. It may be reasonable to ignore ageing for flight concept demonstrators, but beware this reality.\nCharging Like cell ageing, charging is a complex subject that we will not attempt to do proper justice. Any cell that is discharged will need to be charged. Charging is typically performed with a CCCV process (constant current, constant voltage).\nDuring the CC phase of a charge, a cell is charged at constant current. A cell\u0026rsquo;s state of charge can rapidly increase during the CC phase. The CC phase ends when the terminal voltage reaches some charge voltage (the maximum voltage limit for the cell). At that point, the charge cycle changes to CV - the charge voltage is maintained until the current drops below some tiny threshold and the cell is declared full.\nDuring the CV phase of a charge, the charge current is constantly decreasing. At decreasing current, it takes increasing time to increase the charge of the battery. This is an asymptotic process - it takes infinite time to fully charge a cell to zero charge current.\nI don\u0026rsquo;t know about you, but asymptotic processes don\u0026rsquo;t seem like a good idea for concepts intended for high tempo operations.\nThis gets us to our final battery bullet from Part 1: Charge rate varies – cells are very slow to top off.\nProgress I know I keep saying that we\u0026rsquo;re nearly through all the background - but this time it is true. We\u0026rsquo;ve justified every single one of our battery bullets from Part 1. You should have an understanding of why each one is true and some intuition about the complexities of cell behavior.\nOf course we aren\u0026rsquo;t done yet. I promised to show how to quantify these effects - and we will do so by computing each one as a contribution to the overall cell energy density knockdown factor. The pieces are in place, we\u0026rsquo;re just about ready to start knocking down the knockdown factors.\nPart 5. Charge Limits In Part 4 of this series, we discussed several cell characteristics that may have seemed unrelated - power limits, cell degradation due to cycling, and charging. In fact, these characteristics conspire to limit how much of a cell\u0026rsquo;s charge is available for use.\nAlthough a cell has a certain rated capacity (typically given in mAh, but we will work in terms of percent of that capacity), for the purposes of conceptual design sizing, some of that capacity is unavailable to us.\nSome of that unavailable charge is the first few percent discharged from a full battery; we call that region the Top of Charge. There is also some unavailable charge that would be the last few percent discharged from a battery; we call that region the Bottom of Charge.\nSome of these limits are more fungible than others. We will start with the firm and move towards the flexible.\nPower Limits for Bottom of Charge In Part 4, we discussed the limits on power that can be discharged from a cell (figure repeated here). We identified that there are at least four causes of these limits (absolute, current, voltage, waste heat) and that these limits vary with depth of discharge.\nThinking in terms of an aircraft, there will be some minimum power required of the cells late in the mission. While this may simply be to maintain cruise flight, it likely involves a higher power requirement such as aborting a landing or arresting the descent in a vertical landing.\nIf that requirement worked out to 175W per cell, then the power limit chart from Part 4 tells us that we can not go past 85% DOD and achieve the required power. If we were to demand more than 175W at 85% - or 175W beyond 85%, then our bus voltage would drop below the cutoff voltage and our power electronics would not be able to command the speed and power required for this mission phase.\nUnfortunately, this means that 15% of our battery is dead weight. We are forced to carry it around with us, but we can not get ourselves into a situation where we use it.\nCell Ageing for Top and Bottom of Charge In Part 4, we also discussed the damage that accrues to a cell from every use. We observed that damage occurs faster for cells discharged at the top and bottom of charge (figure repeated here).\nJ. Schmalstieg, S. Käbitz, M. Ecker and D. U. Sauer, \u0026lsquo;From accelerated aging tests to a lifetime prediction model: Analyzing lithium-ion batteries,\u0026rsquo; 2013 World Electric Vehicle Symposium and Exhibition (EVS27), 2013\nThe aircraft designer must choose the conditions that define the battery end of life. This will correspond to a certain amount of capacity fade (say 15%) and a certain amount of resistance growth (say 20%). This capacity fade and resistance growth will factor into the cell knockdown factors at a later time. In addition, the designer must consider how many cycles the cells must survive for the economic case to close. For example, do you need to hit 3000 cycles, or can you afford to replace packs at 1000 cycles?\nFor this cell to reach EOL at 3000 cycles, we will need to restrict our cycles to be between 20% and 80% SOC (note that SOC=100%-DOD). I.e. we need to avoid the first 20% and last 20% of the cell to maximize life.\nThe bottom of charge restriction for life is fortunately not very severe. First, it typically substantially overlaps with the limit already imposed by power. Second, most aircraft sizing missions require some sort of reserve - a mission segment that must be able to be flown, but that is not flown frequently. Placing this reserve in a portion of a cell with rapid damage accrual may be acceptable because the reserve is not used frequently. Of course, we still expect the high power draw requirement to apply at the end of any reserve mission.\nConversely, the top of charge restriction for life is painful. Maximizing cell life requires that you avoid topping off your pack and instead size with the assumption that you start missions with a pack that is only 80 to 90% full.\nObviously, cell ageing presents complex tradeoffs for the designer. What defines cell end of life? How many cycles to replacement? How do we operate our packs to maximize life?\nRapid Charge for Top of Charge As discussed in Part 4, the constant voltage (CV) portion of a charge cycle is very slow to top off a cell. For some systems and conops, this will pose no obstacle. However, for missions and conops where many sorties, quick turnaround, fast tempo, and rapid charging are important, you will want to avoid or limit time spent charging in this mode.\nOne interesting perspective is to consider the energy added during charge as incremental miles of range - and then to consider how quickly each mile is added (miles of range per minute of charge).\nLike ageing, charging rate is a part of more complex trades, but it can contribute to a restriction on the usable charge range for a pack.\nRepresentative eVTOL Mission We will introduce an extremely simple eVTOL mission profile along with some other assumptions that will provide an example case for the rest of this series.\nThis mission includes a primary segment followed by a reserve mission requiring a divert. Each segment is made up of a takeoff, cruise, and landing segment. Each segment is specified in terms of time and power level as given below.\nSegment Duration Power (m) (hp) Takeoff Hover 1 500 Cruise 20 50 Landing Hover 1 500 Reject 1 500 Divert 5 50 Landing Hover 1 500 The battery will reach end of life when it reaches 10% capacity fade or 20% resistance growth.\nThe cell usable charge will be restricted to avoid 10% at top of charge and 15% at bottom of charge.\nPartial Discharge Knockdown We are finally ready to calculate our first cell energy knockdown factor. The partial discharge knockdown defined as the usable energy divided by the total cell energy. Recall that the total cell energy is the area under the $OCV$ curve (the grey line in the figure below). The pink regions indicate the un-usable discharge - leaving the usable energy as the white space between them.\nFor mental calculations, we can assume that each portion of charge contains equal energy, allowing us to approximate the partial energy knockdown as the usable charge fraction.\n$$k_{e,DOD}\\approx BOC-TOC$$$$k_{e,DOD}\\approx0.85-0.1=\\,0.75$$Of course, the $OCV$ is not constant and we have gone to lengths to understand that different portions of a cell\u0026rsquo;s charge store different energy. If we calculate the running total energy available in a cell (normalized by the total), we would get a curve like this:\nThis curve starts out steeper than the equal distribution curve because the top of charge contains more energy per charge than the cell average.\nAt 10% DOD, we are at perhaps 11% energy, and at 85% DOD, we are at perhaps 87% energy - we subtract these and adjust our estimate of the partial discharge knockdown to 0.76.\nThis figure is hard to read with great precision. So I have subtracted the equal distribution curve from the running total to arrive at a figure that magnifies the quantities of interest.\nUsing this figure, we can calculate the partial discharge knockdown factor.\n$$\\begin{matrix} {k_{e,DOD}=}\u0026{BOC+D\\left(BOC\\right)}\\\\ \u0026{-\\left(TOC+D\\left(TOC\\right)\\right)} \\end{matrix}$$$$\\begin{matrix} {k_{e,DOD}=}\u0026{0.85+0.024}\\\\ \u0026{-\\left(0.1+0.011\\right)}\\\\ {\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,=}\u0026{0.763}\\\\ \\end{matrix}$$While there are several more knockdown factors (more bad news) yet to come, this one is usually the hardest pill to swallow (this was the worst of it).\nStill With Me? It has taken a while to get to this point, but we\u0026rsquo;ve discussed the cell behaviors that make them a challenge for aircraft design. We introduced the knockdown factor as our primary metric of interest. Now we\u0026rsquo;re starting to quantify those effects. Things are going to move fast from here on.\nIf you made it this far, leave me a note and tell me what you think.\nIf you find this thought provoking, hit share and add your thought as a comment.\nPart 6. Roadmap In Part 3, we introduced the idea of a cell specific energy knockdown factor that captures a variety of phenomena relevant for battery performance and aircraft design. We are working our way through each of these phenomena, calculating how each one contributes to the overall knockdown factor. In Part 5, we developed the cell partial discharge knockdown factor.\nCapacity Fade Knockdown When we defined our representative mission in Part 5, we defined battery end of life as occurring when the cell reaches 10% capacity fade or 20% resistance growth. In our analysis, we will assume the cell has reached both of those limits at EOL.\nThe cell capacity fade knockdown factor is too simple to be called a derivation, it is simply the fraction of cell capacity remaining at end of life. For our case, this is 90%.\n$$k_{Q}=0.9$$One-Hour Discharge Rates Battery people often work and communicate in terms of a discharge current scaled to the size of a given cell. They define the current required to fully discharge a cell (at constant current) in one hour as the 1C current for that cell. If you know a cell\u0026rsquo;s capacity, then it is trivial to calculate that cell\u0026rsquo;s 1C rate - a 4200 mAh cell has a 1C discharge rate of 4.2A.\nA similar idea can be applied to a constant power discharge. We will define the power required to fully discharge a cell (at constant power) in one hour as the 1E power for that cell. Unfortunately, calculating the 1E power is not trivial - it requires numerically solving over the discharge integral. However, since aircraft fly at power settings (not current settings), it is a more useful quantity.\nWe will also need to know the E rate required for a sized battery to complete a given mission. Of course, this whole series is about sizing a battery - so if we need to know the battery size to calculate the battery size, things are going to get iterative.\nAs an initial guess, we will do some back of the envelope calculations. First, we need to know the total energy required to fly the example mission. We simply sum the products of the time and powers for each segment. Don\u0026rsquo;t worry about the horrible units, they will cancel out in a moment. Our mission requires 3250 hp-m of energy.\nSegment Duration Power Energy Power (m) (hp) (hp-m) (E-Rate) Takeoff Hover 1 500 500 6.23 Cruise 20 50 1000 0.623 Landing Hover 1 500 500 6.23 Reject 1 500 500 6.23 Divert 5 50 250 0.623 Landing Hover 1 500 500 6.23 Total 3250 Next, we need to make some adjustments for the size of the cell. That is the crux of these knockdown factors (complicating the iterative process), but we can at least take some first steps. We will use our crude estimate from Part 5 of the partial discharge knockdown factor as well as our capacity fade knockdown factor.\n$$P_{1E}\\approx\\frac{1}{\\,\\left(0.75\\right)\\,\\left(0.9\\right)}\\frac{3250}{60}$$To obtain our estimate of the 1E power required of our sized pack, we divide the total energy requirement by these adjustment factors and also by 60 minutes (to establish the one-hour rate). The 1E power for this vehicle is about 80.25 hp. Unsurprisingly, the cruise occurs at an E rate substantially less than 1.0 (0.623).\nFinite Rate Knockdown In Part 2, we recognized the area under the discharge curve on voltage vs. capacity axes as the useful energy provided by the cell during that discharge. In Part 4, we identified the area under the $OCV$ curve as the reversible energy stored in a cell.\nThese are both total (integral) measures - the total energy discharged and the total energy available. If we take their ratio, we would obtain some measure of the cell efficiency for a discharge. This would be a knockdown factor that accounts for the effects of a finite rate discharge.\nHere the black discharge curve is the discharge profile for our example vehicle introduced in Part 5. The discharge energy required to complete the mission is the area in grey. The area under the corresponding portion of the $OCV$ curve includes the pink and grey areas.\nWhile we can numerically integrate a discharge profile to arrive at the finite rate knockdown factor, that does not provide us with much insight into what is happening during different mission segments and their relative impact on battery performance.\nCell Instantaneous Efficiency We can extend this idea to a single instant during a discharge. The arrows indicate the terminal voltage and the $OCV$ during the second high power discharge of the mission (the nominal landing hover). The ratio of these voltages is the cell discharge efficiency at that instant of the mission.\n$$\\eta_{i}=\\frac{V}{OCV}$$For aircraft performance and sizing, we are usually concerned with discharge at a certain power level. We can put the instantaneous efficiency in terms of a desired power draw.\n$$\\eta_{i}=\\frac{1}{2}+{\\sqrt{\\frac{1}{4}-\\frac{R_{i}\\,P}{OCV^{2}}}}$$This equation makes clear the importance of low internal resistance for efficient discharge at high power.\nFinite Rate and Resistance We will make two modifications to this equation with the goal of simplifying and isolating things that change during a mission or the life of a battery from things that are constant for a given cell. First, we will replace the cell internal resistance with a resistance growth factor applied to the cell internal resistance of a brand new cell. Second, we will replace the discharge power with the discharge E rate with the power for a 1E discharge.\n$$\\eta_{i}=\\frac{1}{2}+{\\sqrt{\\frac{1}{4}-\\frac{k_{R}\\,E_{rate}\\,R_{i,0}\\,P_{1E}}{OCV^{2}}}}$$Of course, the BOL cell internal resistance ($R_{i,0}$) and $OCV$ are functions of depth of discharge, but we have dropped the $f(x)$ notation for clarity.\nWe observe that the resistance growth factor ($k_R$) and the discharge E rate appear as a product - if we treat them as a composite quantity, the effect of a 20% increase in $k_R$ is indistinguishable from the effect of a 20% increase in E rate.\nRecall that our mission profile and battery assumptions from Part 5 defined battery end of life as occurring when the cell resistance grew by 20% - i.e. $k_R=1.2$. This equation demonstrates that an EOL cell discharging at 5E will achieve the same instantaneous efficiency as a BOL cell discharging at 6E.\nWe can generate a plot of cell instantaneous efficiency parameterized by the composite quantity ($k_R\\,E_{rate}$), shown in the black lines below.\nIn this figure, additional grey lines are included to illustrate the effect of the cell cutoff voltage - the minimum voltage power limit. Other power limits could be plotted in similar fashion.\nAlthough the black lines in this figure appear remarkably flat over a wide range of DOD, that is not a general result. It is just a lucky coincidence for this cell. Alternatively, we can plot this same information parameterized by depth of discharge, as a function of rate.\nThe fact that the curves were remarkably flat in the prior figure leads to the lines for different depth of discharge nearly collapsing in this figure.\nTo calculate the instantaneous efficiency for each mission segment at the battery end of life, we multiply the segment E rate by the EOL resistance growth factor. For cruise, this gives $k_R\\, E_rate=1.2\\*0.623=0.7476$; and for hover, 7.476.\nUsing the above chart, we see that instantaneous cell efficiency during cruise is about 99% while during hover it is about 88%. We can add this information to our mission profile table.\nSegment Duration Power Energy Power ηi (m) (hp) (hp-m) (E-Rate) Takeoff Hover 1 500 500 6.23 0.886 Cruise 20 50 1000 0.623 0.990 Landing Hover 1 500 500 6.23 0.884 Reject 1 500 500 6.23 0.882 Divert 5 50 250 0.623 0.989 Landing Hover 1 500 500 6.23 0.877 To obtain the integrated knockdown factor discussed earlier in this article, we would ideally integrate the instantaneous efficiency throughout the mission. Alternatively, we can compute an average efficiency weighted by the energy expended in each mission segment according to the following equation.\n$$k_{e,FR\\\u0026R}=\\frac{\\sum_{i}^{n}E_{i}}{\\sum_{i}^{n}\\frac{E_{i}}{\\eta_{i}}}$$This gives us the cell energy knockdown factor for the effects of both finite rate discharge and resistance growth. Running the numbers yields 0.92 for this value.\n$$k_{e,FR\\\u0026R}=0.92$$Light at the End of the Tunnel If you\u0026rsquo;ve made it this far, congratulations. You\u0026rsquo;re almost done. We now know how to calculate three contributions to the cell energy knockdown factor (covering four physical phenomena). Next week, we should wrap this story up.\nPlease share this series with anyone you think might benefit - understanding of these concepts if fundamental to success designing a battery electric aircraft.\nPart 7. Series Finale Six weeks ago, we started a journey to better understand battery performance in terms of aircraft design and performance. We started with a list of pertinent differences between batteries and liquid fuel. In the following articles we built an intuitive understanding of what causes each difference; at the same time, we laid the foundation for quantifying these differences. We introduced an absolute reference for cell energy and the idea of a knockdown factor to track how a cell\u0026rsquo;s realized performance in a given application differs from the manufacturer\u0026rsquo;s laboratory ratings. In recent articles, we have developed formula to calculate several contributions to the knockdown factor and we are applying what we have learned to a representative vehicle. Today we will fill in the remaining terms in the knockdown factor, and we will bring this story to a close.\nManufacturer\u0026rsquo;s Rated Discharge In Part 3, we discussed how manufacturers determine the specific energy of a cell. They measure the energy obtained from a specific discharge profile and divide that by the cell mass.\nIn Part 4, we introduced the reversible cell energy to serve as an absolute reference for calculations. However, the knockdown factor is the ratio of the realized cell performance to the manufacturer\u0026rsquo;s claims - not to an absolute reference.\nJust as our aircraft\u0026rsquo;s finite rate discharge incurs certain losses, the manufacturer\u0026rsquo;s standard discharge incurs losses.\nManufacturers typically use a full-depth and constant current discharge to determine the cell\u0026rsquo;s energy. Full-depth discharges terminate when the cell terminal voltage reaches the stated cutoff voltage; of course voltage drops with current, so higher rate discharges will reach the cutoff sooner (in terms of capacity). Cells considered \u0026rsquo;energy cells\u0026rsquo; are typically discharged at a relatively low rate - say 0.2C; while cells considered \u0026lsquo;power cells\u0026rsquo; are typically discharged at a higher rate - say 1C.\nIf you plot the cell $OCV$ on the cell\u0026rsquo;s constant current discharge rate map, you could calculate the manufacturer\u0026rsquo;s claims by comparing the area under the discharge curve to the area under the $OCV$ curve. Of course it is difficult to calculate ratios of areas by looking at a chart. Instead, we can estimate this contribution to the cell knockdown factor with this simple equation.\n$$k_{e,mfg}=\\frac{E_{S,c}}{E_{rev}}\\approx1-\\frac{Q\\,I\\,R_{i}}{E_{rev}}$$If more accuracy is desired, we can numerically simulate the manufacturer\u0026rsquo;s discharge. This has been done for a range of discharge currents to produce the following figure.\nThe premature cutoff effect mentioned earlier is illustrated by the grey curve in this figure. This effect is neglected by the simple approximation provided by the prior equation.\nThe manufacturer\u0026rsquo;s rated discharge knockdown factor as calculated by numerical integration is given by the black curve in this figure. For our power cell, this effect is small, but worth computing - for an energy cell, this effect can likely be neglected.\n$$k_{e,mfg}=0.9743$$Pack Mass Overhead As installed in an aircraft, battery packs contain more than just cells. Everything in a pack that is not a cell contributes to the pack mass overhead. This will include provisions for current collection, pack structure, thermal protection and management, the BMS, etc.\nThe pack mass knockdown factor is simply the total cell mass (number of cells times the mass of a single cell) divided by the battery pack mass.\n$$k_{m}=\\,\\frac{N_{c}\\,m_{c}}{m_{b}}$$Exactly what is book-kept as pack mass vs. airframe mass can get a bit messy. If an aircraft has a removable pack, I would suggest starting by considering everything that comes off when a pack is removed is the pack mass - and everything left behind is part of the airframe. These details do not matter for this discussion - every pack will have some overhead mass.\nThe pack mass overhead is likely one of the most familiar contributions to the knockdown factor. Many discussions center around whether a battery specific energy level is specified at the cell level or the pack level - the pack mass overhead is exactly this difference. Practitioners often think and communicate in terms of pack \u0026lsquo;overhead\u0026rsquo; - more formally called the \u0026lsquo;pack non-cell mass fraction\u0026rsquo;. Advanced packs have an overhead of about 15-20%.\nOur knockdown factor calculation works in terms of the \u0026lsquo;pack cell mass fraction\u0026rsquo; - which is calculated as one minus the overhead. Advanced packs will have a pack cell mass fraction of about 80-85%. For our example, we will assume a pack with 18% overhead.\n$$k_{m}=0.82$$Cell Energy Knockdown Factor We now have all the parts required to assemble our cell energy knockdown factor. Each contribution represents an independent effect referenced to the absolute reference energy (except for the mass contribution) and so they can be combined by multiplying them together - except for the manufacturer\u0026rsquo;s rated discharge knockdown factor, which must appear in the denominator.\n$$k=\\,\\frac{k_{m}\\,k_{e,DOD}\\,k_{e,FR\\\u0026R}\\,k_{Q}}{k_{e,mfg}\\,}$$Plugging in the five terms calculated for the example case over the past few articles gives us a combined knockdown factor of 0.532.\n$$k=\\,\\frac{\\left(0.82\\right)\\,\\left(0.763\\right)\\,\\left(0.92\\right)\\,\\left(0.9\\right)}{0.9743\\,}=0.532$$For our example cell, the manufacturer\u0026rsquo;s rated specific energy is 230 Wh/kg - but in this installation, the aircraft achieves a pack specific energy of 122 Wh/kg.\nOur example mission required 3250 hp-m of energy from the battery - which is a bit over 40 kWh. Our aircraft would need a 330 kg (727 lb) pack.\nWithout the context provided by the vehicle mass and the reasonableness of the hover and cruise powers, this doesn\u0026rsquo;t mean a whole lot. That is on purpose. I leave those things out because the focus here should not be on the merits of the example vehicle, but instead on how these calculations can be performed for any candidate vehicle.\nOur knockdown factor provides a straightforward way to size a battery pack for an electric aircraft. It includes effects of pack mass overhead, restricted depth of discharge for power limits and a variety of operational considerations, cell finite rate efficiency (including resistance growth at EOL), and capacity fade at EOL.\nBetter than a black-box calculation of all these effects, the knockdown factor buildup approach provides transparency into each effect and its relative contribution to the pack size. Hopefully you have also gained some intuition as to what factors influence each contribution and what you might do as a designer to effect change.\nAlthough it has not been a focus of this discussion, I hope it is apparent how much of an effect conops and mission requirements have on these calculations. A small UAS may have minimal pack overhead and could use a larger fraction of the cell capacity. EOL considerations may not matter - allowing the vehicle performance to fade as the cells age. This situation will result in a very different knockdown factor and realized battery specific energy. These are decisions that are subject to trade.\nConclusion This series was motivated by the differences between liquid fuel and batteries for aircraft propulsion. While it may seem like we have lost track of that motivation, I hope that is not the case. Every pound of liquid fuel contains the same energy - it does not matter which part of the tank it comes out of, how old the tank is, or how fast you burn it. Put another way, the specific energy knockdown factor for liquid fuel is 1.0.\nResponsible conceptual designers of battery electric aircraft need to understand these effects and quantify them in their sizing calculations. Failure to do so will result in aircraft that fail to meet design expectations.\nAlthough this is a good place to stop this series of articles, there is much more to be considered when designing an electric aircraft. Perhaps there will be another article series down the road. If you think that is a good idea, leave a comment and let me know what you would like to see covered.\n","permalink":"https://mcdonaldaerospace.com/projects/batteries_not_fuel/","summary":"Battery behavior from the perspective of aircraft design.","title":"Batteries Are Not Fuel"},{"content":"Also available organized by year.\nAerodynamicsAircraft DesignCHTLSEducationElectric PropulsioneVTOLOpenVSPPatentStudent ResearchSystems Visualization InterfaceThermodynamicsUncertainty \u0026amp; MDOAerodynamics Experimental and Computational Investigation of Stacked Rotor Performance in Hover G. Jacobellis, R. Singh, C. Johnson, J. Sirohi, and R. McDonaldAerosp. Sci. Technol. 2021Combined experimental and computational study of coaxial stacked rotor aerodynamics in hover. Provides validated performance data relevant to compact eVTOL rotor configurations. Experimental and Computational Investigation of Stacked Rotor Acoustics in Hover G. Jacobellis, R. Singh, C. Johnson, J. Sirohi, and R. McDonaldVFS Forum 2020 Investigation of Stacked Rotor Performance in Hover Part 1: Experimental Measurements C. Johnson, J. Sirohi, G. Jacobellis, R. Singh, and R. McDonaldVFS Forum 2020 Investigation of Stacked Rotor Performance in Hover Pt. II: Computational Validation G. Jacobellis, R. Singh, C. Johnson, J. Sirohi, and R. McDonaldAHS Aeromechanics 2020 Development of an Interactive Wave Drag Capability for the OpenVSP Parametric Geometry Tool M. Waddington and R. A. McDonaldAIAA Aviation 2015 Aerodynamic Shape Optimization of Propulsion–Airframe Integration While Matching Lift Distribution A. M. Gary and R. A. McDonaldAIAA SciTech 2014 Flight Testing Small UAVs for Aerodynamic Parameter Estimation A. Chase and R. A. McDonaldAIAA AFM 2014 A Meshless Finite Difference Scheme for Compressible Potential Flows A. Ramos and R. McDonaldAIAA 2011 Constrained Hermite Interpolation for Mesh-Free Derivative Estimation Near and On Boundaries R. A. McDonald and A. RamosAIAA J. 2011 A Three-Dimensional Vortex Particle–Panel Method for Modeling Propulsion–Airframe Interaction J. Calabretta and R. McDonaldAIAA SciTech 2010 Lift Superposition and Aerodynamic Twist Optimization for Achieving Desired Lift Distributions K. Lane, D. Marshall, and R. McDonaldAIAA SciTech 2010 Formulation, Realization, and Demonstration of a Process to Generate Aerodynamic Metamodels for Hypersonic Cruise Vehicle Design R. A. McDonald and D. N. MavrisSAE WAC 2000 Aircraft Design Battery Knockdown Factors for Conceptual Design R. A. McDonaldAIAA Aviation 2024Develops and quantifies battery knockdown factors — the gap between cell-level energy density and what is actually usable at the pack level in conceptual design. Provides practical sizing multipliers accounting for thermal management, depth of discharge limits, and aging. Electrified Lift-Plus-Cruise Aircraft Sizing with Varying Battery Modeling Assumptions I. Chakraborty, A. A. Mishra, and R. A. McDonaldAIAA SciTech 2024Examines how different battery model fidelity assumptions — from simple specific energy to full electrochemical models — propagate into differences in vehicle sizing for a lift-plus-cruise eVTOL configuration. Batteries Are Not Fuel R. A. McDonaldengrXiv 2023A conceptual paper examining the fundamental differences between battery-stored energy and chemical fuel from an aircraft design perspective. Argues that treating batteries as a drop-in fuel replacement leads to incorrect intuitions about performance, range, and sizing — and develops the correct frameworks. Future Aircraft Concepts and Design Methods R. A. McDonald, B. J. German, T. Takahashi, C. Bil, W. Anemaat, A. Chaput, R. Vos, and N. HarrisonAeronautical Journal 2022A broad survey of emerging aircraft concepts — electric, hybrid-electric, urban air mobility, supersonic, and autonomous vehicles — and the design methods needed to evaluate them at the conceptual stage. Open Vehicle Sketch Pad: An Open Source Parametric Geometry and Analysis Tool for Conceptual Aircraft Design R. A. McDonald and J. R. GloudemansAIAA SciTech 2022Comprehensive overview paper describing OpenVSP capabilities, architecture, and applications. Covers geometry parameterization, analysis integration, scripting, and the broader ecosystem of tools that interface with VSP. Modeling of Electric Motor Driven Variable Pitch Propellers for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2016 Modeling of Electric Motor Driven Propellers for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2015 Optimal Propeller Pitch Scheduling and Propeller–Airframe Matching for Conceptual Design R. A. McDonaldAIAA Aviation 2015 Aerodynamic Shape Optimization of Propulsion–Airframe Integration While Matching Lift Distribution A. M. Gary and R. A. McDonaldAIAA SciTech 2014 Electric Propulsion Modeling for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2014Develops system-level models for electric propulsion components — motors, controllers, gearboxes, and batteries — suitable for integration in conceptual aircraft sizing codes. Companion to the electric motor modeling paper. Impact of Advanced Energy Technologies on Aircraft Design R. A. McDonald, A. T. Chase, C. Green, and M. WaddingtonAIAA SciTech 2014 Low Energy Nuclear Reaction Aircraft: 2013 ARMD Seedling Fund Phase I Project D. P. Wells, R. McDonald, R. Campbell, A. Chase, J. Daniel, M. Darling, C. Green, C. MacGregor, P. Sudak, H. Sykes, et al.NASA/TM–2014-218283 Electric Motor Modeling for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2013First paper in a series developing physics-based motor models for conceptual design. Establishes specific power and efficiency scaling laws from motor geometry and electromagnetic principles. Enabling Rapid Conceptual Design Using Geometry-Based Multi-Fidelity Models in VSP J. BelbenAIAA SciTech 2013 Establishing Mission Requirements Based on Consideration of Aircraft Operations R. A. McDonaldJ. Aircraft 2013Journal version of the mission-requirements work, extending the conference paper to a full treatment of how operational considerations should shape aircraft design requirements — including fleet dispatch reliability and time-of-day traffic patterns. Solar Energy Collection Analysis Tool for Conceptual Aircraft Design G. Glazebrook and R. McDonaldAIAA SciTech 2013 Aircraft Operations Based Mission Requirements R. A. McDonaldAIAA SciTech 2012 Fundamental Sizing Implications of Constant Weight Aircraft R. A. McDonaldAIAA ATIO 2012Analyzes how the constant-weight constraint of battery-electric aircraft (fuel doesn\u0026#39;t burn off) fundamentally changes sizing behavior relative to conventional aircraft — including range, payload fractions, and structural sizing. Mission Performance Considered as Point Performance in Aircraft Design R. A. McDonaldJ. Aircraft 2011Derives the conditions under which integrated mission performance (range, endurance) can be computed from instantaneous point-performance analysis — enabling faster design-space exploration without full mission simulation. Conceptual Design of a Next Generation, 150 Passenger Commercial Transport R. Halper, K. Lane, D. Marschik, B. Morham, J. Pham, R. McDonald, and B. WrightAIAA SciTech 2010 Conceptual Design of an Environmentally Responsible 150-Passenger Commercial Aircraft N. Smith, B. Blessing, J. Dixon, A. Mackey, G. McKenzie, R. McDonald, and B. WrightAIAA SciTech 2010 Designing a Green Aircraft: Cal Poly\u0026#39;s 2009 Undergraduate Aircraft Designs R. McDonald and B. WrightAIAA SciTech 2010 Geometry Needs of Conceptual Aircraft Design — Panel Discussion A. Hahn and R. McDonaldAIAA SciTech 2010 Lift Superposition and Aerodynamic Twist Optimization for Achieving Desired Lift Distributions K. Lane, D. Marshall, and R. McDonaldAIAA SciTech 2010 Mission Performance as Point Performance R. A. McDonaldAIAA ATIO 2010 Parameter Estimation of Fundamental Technical Aircraft Information Applied to Aircraft Performance M. Vallone and R. McDonaldAIAA SciTech 2010 Multidisciplinary Design Optimization of an Extreme Aspect Ratio HALE UAV B. Morrisey and R. McDonaldAIAA ATIO 2009 Underpowered Aircraft — Performance and Operational Possibilities A. Ezzard, M. Vallone, and R. McDonaldAIAA SciTech 2009 The Role of Error in the Conceptual Design of a Transport Aircraft R. McDonaldAIAA SciTech 2007 CHTLS A Meshless Finite Difference Scheme for Compressible Potential Flows A. Ramos and R. McDonaldAIAA 2011 Constrained Hermite Interpolation for Mesh-Free Derivative Estimation Near and On Boundaries R. A. McDonald and A. RamosAIAA J. 2011 Education Conceptual Design of a Next Generation, 150 Passenger Commercial Transport R. Halper, K. Lane, D. Marschik, B. Morham, J. Pham, R. McDonald, and B. WrightAIAA SciTech 2010 Conceptual Design of an Environmentally Responsible 150-Passenger Commercial Aircraft N. Smith, B. Blessing, J. Dixon, A. Mackey, G. McKenzie, R. McDonald, and B. WrightAIAA SciTech 2010 Designing a Green Aircraft: Cal Poly\u0026#39;s 2009 Undergraduate Aircraft Designs R. McDonald and B. WrightAIAA SciTech 2010 Senior Design at Cal Poly: A Recipe for Success R. McDonald, J. Puig-Suari, D. Esposto, and B. WrightAIAA SciTech 2009 Electric Propulsion Battery Knockdown Factors for Conceptual Design R. A. McDonaldAIAA Aviation 2024Develops and quantifies battery knockdown factors — the gap between cell-level energy density and what is actually usable at the pack level in conceptual design. Provides practical sizing multipliers accounting for thermal management, depth of discharge limits, and aging. Electrified Lift-Plus-Cruise Aircraft Sizing with Varying Battery Modeling Assumptions I. Chakraborty, A. A. Mishra, and R. A. McDonaldAIAA SciTech 2024Examines how different battery model fidelity assumptions — from simple specific energy to full electrochemical models — propagate into differences in vehicle sizing for a lift-plus-cruise eVTOL configuration. Batteries Are Not Fuel R. A. McDonaldengrXiv 2023A conceptual paper examining the fundamental differences between battery-stored energy and chemical fuel from an aircraft design perspective. Argues that treating batteries as a drop-in fuel replacement leads to incorrect intuitions about performance, range, and sizing — and develops the correct frameworks. Future Aircraft Concepts and Design Methods R. A. McDonald, B. J. German, T. Takahashi, C. Bil, W. Anemaat, A. Chaput, R. Vos, and N. HarrisonAeronautical Journal 2022A broad survey of emerging aircraft concepts — electric, hybrid-electric, urban air mobility, supersonic, and autonomous vehicles — and the design methods needed to evaluate them at the conceptual stage. eVTOL Stored Energy Overview R. McDonald and B. GermanUber Elevate Summit 2017Presentation at the first Uber Elevate Summit covering the fundamental energy storage requirements for urban air mobility eVTOL vehicles and the technology gap relative to available battery systems. Modeling of Electric Motor Driven Variable Pitch Propellers for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2016 Modeling and Test of the Efficiency of Electronic Speed Controllers for Brushless DC Motors C. R. Green and R. A. McDonaldAIAA Aviation 2015 Modeling of Electric Motor Driven Propellers for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2015 Optimal Propeller Pitch Scheduling and Propeller–Airframe Matching for Conceptual Design R. A. McDonaldAIAA Aviation 2015 Electric Propulsion Modeling for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2014Develops system-level models for electric propulsion components — motors, controllers, gearboxes, and batteries — suitable for integration in conceptual aircraft sizing codes. Companion to the electric motor modeling paper. Impact of Advanced Energy Technologies on Aircraft Design R. A. McDonald, A. T. Chase, C. Green, and M. WaddingtonAIAA SciTech 2014 Electric Motor Modeling for Conceptual Aircraft Design R. A. McDonaldAIAA SciTech 2013First paper in a series developing physics-based motor models for conceptual design. Establishes specific power and efficiency scaling laws from motor geometry and electromagnetic principles. Establishing Mission Requirements Based on Consideration of Aircraft Operations R. A. McDonaldJ. Aircraft 2013Journal version of the mission-requirements work, extending the conference paper to a full treatment of how operational considerations should shape aircraft design requirements — including fleet dispatch reliability and time-of-day traffic patterns. Solar Energy Collection Analysis Tool for Conceptual Aircraft Design G. Glazebrook and R. McDonaldAIAA SciTech 2013 Aircraft Operations Based Mission Requirements R. A. McDonaldAIAA SciTech 2012 Fundamental Sizing Implications of Constant Weight Aircraft R. A. McDonaldAIAA ATIO 2012Analyzes how the constant-weight constraint of battery-electric aircraft (fuel doesn\u0026#39;t burn off) fundamentally changes sizing behavior relative to conventional aircraft — including range, payload fractions, and structural sizing. eVTOL Aerial Vehicle with Differential Control Mechanisms T. Akers, P. Kalogiannis, M. Moore, R. A. McDonald, and I. A. VillaUS Patent 12,110,106, 2024 Battery Knockdown Factors for Conceptual Design R. A. McDonaldAIAA Aviation 2024Develops and quantifies battery knockdown factors — the gap between cell-level energy density and what is actually usable at the pack level in conceptual design. Provides practical sizing multipliers accounting for thermal management, depth of discharge limits, and aging. Electrified Lift-Plus-Cruise Aircraft Sizing with Varying Battery Modeling Assumptions I. Chakraborty, A. A. Mishra, and R. A. McDonaldAIAA SciTech 2024Examines how different battery model fidelity assumptions — from simple specific energy to full electrochemical models — propagate into differences in vehicle sizing for a lift-plus-cruise eVTOL configuration. Batteries Are Not Fuel R. A. McDonaldengrXiv 2023A conceptual paper examining the fundamental differences between battery-stored energy and chemical fuel from an aircraft design perspective. Argues that treating batteries as a drop-in fuel replacement leads to incorrect intuitions about performance, range, and sizing — and develops the correct frameworks. Routing Based on Aerial Vehicle Characteristics A. T. Chase, I. A. Villa, L. A. Wilhelm, J. Petersen, R. A. McDonald, M. D. Moore, and C. MikolajczakUS Patent 11,804,141, 2023 Aerial Vehicle Using Motor Pulse-Induced Cyclic Control R. A. McDonald, M. Moore, and I. A. VillaUS Patent 11,345,469, 2022 Conformal Pylon/Boom Prop-Rotors R. A. McDonaldUS Patent 11,465,737, 2022 Future Aircraft Concepts and Design Methods R. A. McDonald, B. J. German, T. Takahashi, C. Bil, W. Anemaat, A. Chaput, R. Vos, and N. HarrisonAeronautical Journal 2022A broad survey of emerging aircraft concepts — electric, hybrid-electric, urban air mobility, supersonic, and autonomous vehicles — and the design methods needed to evaluate them at the conceptual stage. Quad-Wing Vertical Takeoff and Landing Aircraft I. A. Villa, M. Moore, R. A. McDonald, H. T. Won, A. Chase, A. M. Gary, and C. SeubertUS Patent 11,267,570, 2022 Experimental and Computational Investigation of Stacked Rotor Performance in Hover G. Jacobellis, R. Singh, C. Johnson, J. Sirohi, and R. McDonaldAerosp. Sci. Technol. 2021Combined experimental and computational study of coaxial stacked rotor aerodynamics in hover. Provides validated performance data relevant to compact eVTOL rotor configurations. Experimental and Computational Investigation of Stacked Rotor Acoustics in Hover G. Jacobellis, R. Singh, C. Johnson, J. Sirohi, and R. McDonaldVFS Forum 2020 Investigation of Stacked Rotor Performance in Hover Part 1: Experimental Measurements C. Johnson, J. Sirohi, G. Jacobellis, R. Singh, and R. McDonaldVFS Forum 2020 Investigation of Stacked Rotor Performance in Hover Pt. II: Computational Validation G. Jacobellis, R. Singh, C. Johnson, J. Sirohi, and R. McDonaldAHS Aeromechanics 2020 eVTOL Stored Energy Overview R. McDonald and B. GermanUber Elevate Summit 2017Presentation at the first Uber Elevate Summit covering the fundamental energy storage requirements for urban air mobility eVTOL vehicles and the technology gap relative to available battery systems. Multidisciplinary Design Optimization of an Extreme Aspect Ratio HALE UAV B. Morrisey and R. McDonaldAIAA ATIO 2009 OpenVSP Advanced Scripting Development and Application of OpenVSP T. Nascenzi, T. Cuatt, and R. A. McDonaldAIAA SciTech 2025 Open Vehicle Sketch Pad: An Open Source Parametric Geometry and Analysis Tool for Conceptual Aircraft Design R. A. McDonald and J. R. GloudemansAIAA SciTech 2022Comprehensive overview paper describing OpenVSP capabilities, architecture, and applications. Covers geometry parameterization, analysis integration, scripting, and the broader ecosystem of tools that interface with VSP. Advanced Modeling in OpenVSP R. A. McDonaldAIAA Aviation 2016 Development of an Interactive Wave Drag Capability for the OpenVSP Parametric Geometry Tool M. Waddington and R. A. McDonaldAIAA Aviation 2015 Interactive Reconstruction of 3D Models in the OpenVSP Parametric Geometry Tool R. A. McDonaldAIAA SciTech 2015 Parametric Identification of Surface Regions in OpenVSP for Improved Engineering Analysis A. M. Gary and R. A. McDonaldAIAA SciTech 2015 User Defined Components in the OpenVSP Parametric Geometry Tool J. R. Gloudemans and R. McDonaldAIAA SciTech 2015 Aerodynamic Shape Optimization of Propulsion–Airframe Integration While Matching Lift Distribution A. M. Gary and R. A. McDonaldAIAA SciTech 2014 Enabling Rapid Conceptual Design Using Geometry-Based Multi-Fidelity Models in VSP J. BelbenAIAA SciTech 2013 Geometry Needs of Conceptual Aircraft Design — Panel Discussion A. Hahn and R. McDonaldAIAA SciTech 2010 Improved Geometry Modeling for High Fidelity Parametric Design J. Gloudemans and R. McDonaldAIAA SciTech 2010 Patent Aerial Vehicle with Differential Control Mechanisms T. Akers, P. Kalogiannis, M. Moore, R. A. McDonald, and I. A. VillaUS Patent 12,110,106, 2024 Routing Based on Aerial Vehicle Characteristics A. T. Chase, I. A. Villa, L. A. Wilhelm, J. Petersen, R. A. McDonald, M. D. Moore, and C. MikolajczakUS Patent 11,804,141, 2023 Aerial Vehicle Using Motor Pulse-Induced Cyclic Control R. A. McDonald, M. Moore, and I. A. VillaUS Patent 11,345,469, 2022 Conformal Pylon/Boom Prop-Rotors R. A. McDonaldUS Patent 11,465,737, 2022 Quad-Wing Vertical Takeoff and Landing Aircraft I. A. Villa, M. Moore, R. A. McDonald, H. T. Won, A. Chase, A. M. Gary, and C. SeubertUS Patent 11,267,570, 2022 Student Research Development of an Interactive Wave Drag Capability for the OpenVSP Parametric Geometry Tool M. Waddington and R. A. McDonaldAIAA Aviation 2015 Modeling and Test of the Efficiency of Electronic Speed Controllers for Brushless DC Motors C. R. Green and R. A. McDonaldAIAA Aviation 2015 Parametric Identification of Surface Regions in OpenVSP for Improved Engineering Analysis A. M. Gary and R. A. McDonaldAIAA SciTech 2015 Aerodynamic Shape Optimization of Propulsion–Airframe Integration While Matching Lift Distribution A. M. Gary and R. A. McDonaldAIAA SciTech 2014 Flight Testing Small UAVs for Aerodynamic Parameter Estimation A. Chase and R. A. McDonaldAIAA AFM 2014 Impact of Advanced Energy Technologies on Aircraft Design R. A. McDonald, A. T. Chase, C. Green, and M. WaddingtonAIAA SciTech 2014 Enabling Rapid Conceptual Design Using Geometry-Based Multi-Fidelity Models in VSP J. BelbenAIAA SciTech 2013 Solar Energy Collection Analysis Tool for Conceptual Aircraft Design G. Glazebrook and R. McDonaldAIAA SciTech 2013 A Meshless Finite Difference Scheme for Compressible Potential Flows A. Ramos and R. McDonaldAIAA 2011 Constrained Hermite Interpolation for Mesh-Free Derivative Estimation Near and On Boundaries R. A. McDonald and A. RamosAIAA J. 2011 A Three-Dimensional Vortex Particle–Panel Method for Modeling Propulsion–Airframe Interaction J. Calabretta and R. McDonaldAIAA SciTech 2010 Conceptual Design of a Next Generation, 150 Passenger Commercial Transport R. Halper, K. Lane, D. Marschik, B. Morham, J. Pham, R. McDonald, and B. WrightAIAA SciTech 2010 Conceptual Design of an Environmentally Responsible 150-Passenger Commercial Aircraft N. Smith, B. Blessing, J. Dixon, A. Mackey, G. McKenzie, R. McDonald, and B. WrightAIAA SciTech 2010 Lift Superposition and Aerodynamic Twist Optimization for Achieving Desired Lift Distributions K. Lane, D. Marshall, and R. McDonaldAIAA SciTech 2010 Parameter Estimation of Fundamental Technical Aircraft Information Applied to Aircraft Performance M. Vallone and R. McDonaldAIAA SciTech 2010 A User Friendly Interface for Gaussian Process Metamodeling C. Baukol, R. McDonald, and N. DelmasAIAA SciTech 2009 Multidisciplinary Design Optimization of an Extreme Aspect Ratio HALE UAV B. Morrisey and R. McDonaldAIAA ATIO 2009 Underpowered Aircraft — Performance and Operational Possibilities A. Ezzard, M. Vallone, and R. McDonaldAIAA SciTech 2009 Systems Visualization Interface A User Friendly Interface for Gaussian Process Metamodeling C. Baukol, R. McDonald, and N. DelmasAIAA SciTech 2009 Cost-Benefit Analysis of Error Reduction for Complex Systems R. McDonaldAIAA ATIO 2009 The Role of Error in the Conceptual Design of a Transport Aircraft R. McDonaldAIAA SciTech 2007 Error Allocation in Complex Systems Design R. McDonaldAIAA MAO 2006 Error Propagation and Metamodeling for a Fidelity Tradeoff Capability in Complex Systems Design R. A. McDonaldGeorgia Tech 2006 Thermodynamics Performance Characterization of Turboshaft Engines Using Work Potential Methods D. W. Riggins, C. D. Wilson, B. A. Roth, and R. A. McDonaldJ. Am. Helicopter Soc. 2005 A Method for Thermodynamic Work Potential Analysis of Aircraft Engines B. Roth, R. McDonald, and D. MavrisAIAA JPC 2002 An Investigation of Applications for Thermodynamic Work Potential Methods D. Mavris, B. Roth, and R. McDonaldGeorgia Tech 2002 Performance Characterization of Turboshaft Engines: Work Potential and Second-Law Analysis B. Wilson, D. Riggins, B. Roth, and R. McDonaldAHS Forum 2002 Uncertainty \u0026amp; MDO Parameter Estimation of Fundamental Technical Aircraft Information Applied to Aircraft Performance M. Vallone and R. McDonaldAIAA SciTech 2010 A User Friendly Interface for Gaussian Process Metamodeling C. Baukol, R. McDonald, and N. DelmasAIAA SciTech 2009 Cost-Benefit Analysis of Error Reduction for Complex Systems R. McDonaldAIAA ATIO 2009 The Role of Error in the Conceptual Design of a Transport Aircraft R. McDonaldAIAA SciTech 2007 Error Allocation in Complex Systems Design R. McDonaldAIAA MAO 2006 Error Propagation and Metamodeling for a Fidelity Tradeoff Capability in Complex Systems Design R. A. McDonaldGeorgia Tech 2006 Formulation, Realization, and Demonstration of a Process to Generate Aerodynamic Metamodels for Hypersonic Cruise Vehicle Design R. A. McDonald and D. N. MavrisSAE WAC 2000 ","permalink":"https://mcdonaldaerospace.com/research/by-topic/","summary":"Technical papers, journal articles, patents, and other publications, organized by topic.","title":"Publications by Topic"},{"content":"Over the years, I\u0026rsquo;ve developed numerous smaller tools that don\u0026rsquo;t deserve an extensive page, but that do deserve to be shared. These tools don\u0026rsquo;t have much in common other than 1) I wrote them, and 2) They might be of interest to an aerospace engineer.\nlibNeuralFoil libNeuralFoil is a C++ library implementation of Peter Sharpe\u0026rsquo;s NeuralFoil. NeuralFoil is a neural network model of airfoil performance trained on a large set of XFoil runs. This library version of NeuralFoil is intended for tight integration into C++ programs without introducing a Python dependency on the resulting binary.\nIn addition to evaluating the NeuralFoil model, libNeuralFoil also has the ability to calculate the first derivatives of the NeuralFoil model \u0026ndash; facilitating use in applications including optimization, iterative solution, and uncertainty propagation.\nGitHub PropDBTools The UIUC Propeller Data Site is a tremendous resource created and maintained by Prof. Michael Selig and students at UIUC. A large number of propellers suitable for application to radio-control aircraft and small UAV\u0026rsquo;s have been tested in the wind tunnel with the results reported in the data site.\nWhile the propeller data (say $C_T$ and $C_P$ vs. $J$) is contained in simple data files, the meta-data for each propeller (say diameter, pitch, and what RPM\u0026rsquo;s were tested) is not explicitly provided. Instead, it is implied by the names of the files containing the data.\nThis layout style makes it very easy for a user to scan the database and to pull out the data they need about a particular propeller. Unfortunately, this style makes it rather challenging for a computer program to scan through and to work on the database as a whole.\nThese tools address that challenge. Originally written in Matlab, this has been ported to Python by Daniel Enriquez and is used under the hood in his online propeller database PropFolio.\nGitHub Matlab File Exchange MATPAN2D MATPAN2D is an attempt to create a fast, simple, and hackable design tool for modeling interesting aerodynamic phenemona including power-effects and inteference between bodies. It is intended to be a teaching and reference implementation — readable, documented, and verifiable. It is a 2D potential flow code capable of either planar or axisymmetric solutions based on the methods in Vortex Element Methods for fluid Dynamic Analysis of Engineering Systems, by R.I. Lewis, 1991.\nGitHub bat-perf bat-perf is a MATLAB implementation of a battery performance model appropriate for conceptual design and performance studies of aircraft. It is a very simple approach, but it captures the required nuance for this purpose.\nIn addition to the core battery model, bat-perf can also calculate specific energy knockdown factors - an interpretable set of metrics that quantify the non-ideal effects incurred when using a battery.\nThe ideas implemented in bat-perf were first published in Batteries Are Not Fuel. Formalism underpinning these ideas was later published as an AIAA Paper - bat-perf (or its predecessors) was used for all of the calculations in these articles.\nGitHub Battery Knockdown Factors for Conceptual Design R. A. McDonaldAIAA Aviation 2024Develops and quantifies battery knockdown factors — the gap between cell-level energy density and what is actually usable at the pack level in conceptual design. Provides practical sizing multipliers accounting for thermal management, depth of discharge limits, and aging. CHTLS - Constrained Hermite Taylor Series Least Squares Like the finite difference method, the Taylor Series Least Squares method can be used to estimate derivatives. The TLS technique can be used to estimate derivatives from scattered or unstructured data. The Hermite Taylor Series Least Squares technique augments the TLS approach with information about the derivative of the function. The Constrained Hermite Taylor Series Least Squares technique augments the HTLS technique by constraining the least squares problem to match the derivative at the point of interest.\nThe CHTLS is capable of calculating surface velocities and thereby pressure from the potential solution in unstructured panel codes. It has been used for this purpose by multiple codes including VSPAERO, CPanel, DUST, and others.\n-Matlab File Exchange\n2011 A Meshless Finite Difference Scheme for Compressible Potential Flows A. Ramos and R. McDonaldAIAA 2011 Constrained Hermite Interpolation for Mesh-Free Derivative Estimation Near and On Boundaries R. A. McDonald and A. RamosAIAA J. 2011 ","permalink":"https://mcdonaldaerospace.com/projects/aero_tools/","summary":"Miscellaneous aerospace tools.","title":"Aero Tools"},{"content":"UnPlotter is a browser-based tool for recovering numerical data from figures in PDF files — the inverse of plotting.\nThe Problem Technical papers, reports, and product data sheets routinely publish data only as figures. Fortunately, these documents are usually published as PDF files with high quality figures included in a vector format. When you need the numbers represented by the curves — to validate a model, compare with your own results, or reproduce an analysis — you\u0026rsquo;re left tracing curves by hand or taking a screenshot and using a raster plot digitizing tool. UnPlotter automates this with an accurate, calibrated workflow.\nHow It Works Load a PDF directly in the browser (nothing is uploaded; processing is local) Define the axis calibration by selecting curves representing x and y extent Select and name the curves you want to export Export as CSV or JSON Axes can be linear or logarithmic. Extract multiple curves per figure with just a few clicks.\nImplementation UnPlotter runs entirely in the browser using JavaScript and the PDF.js library for rendering and parsing. No server, no data upload, no account required.\nLinks unplotter.com — try it GitHub — source code ","permalink":"https://mcdonaldaerospace.com/projects/unplotter/","summary":"Extract numerical data from figures in PDF files.","title":"UnPlotter"},{"content":"Plotting is a fundamental mode of technical communication (along with writing, speaking, drawings, equations, and code). Good plots can effortlessly convey complex topics, while bad plots can ruin you. Over the years, I\u0026rsquo;ve developed a handful of little utilities to help me, my team, and my students make prettier plots.\nHatched Lines Long ago (~January 2006), I needed to produce quality graphics in Java to represent a constrained optimization problem. In this style, a constraint line is drawn with hatches marking the \u0026ldquo;bad\u0026rdquo; side of the line. My need to generate quality graphics representing constrained optimization problems keeps coming back. In December 2006, pained by witnessing my students drawing hatches on lines with PhotoShop, I wrote a Matlab version of this tool including a helper for working with constraint data. Most recently (March 2019), my team once again needed to visualize constrained design spaces; this time in Python and Matplotlib. So, in a bit of déjà vu, I wrote the same tool for a third time.\nJava The Java version is implemented as a custom Graphics2D Stroke that draws hatches along a line as the line itself is drawn. Consequently, anything drawn with Java\u0026rsquo;s Graphics2D can use this custom line style. Others have done much more creative things with custom strokes.\nGitHub I also have a couple of 3D versions of this, one in Java3D, the other using a simple software renderer.\nMatlab The Matlab version includes a function hatchedline that is roughly a drop-in replacement for plot and also a helper hatchedcontours to plot contour data with hatched lines. Importantly, Matlab contour data is not oriented, so there is also ocontourc to orient the contour lines consistently.\nGitHub Matlab File Exchange Python Similar to the Java approach, the Python version it is implemented as a PathEffect in Matplotlib and should be applicable to any line drawn. I got this feature included in the Matplotlib project in version 3.4.0, so if you use Matplotlib you should already have this.\nIn Python, \u0026lsquo;hatches\u0026rsquo; refer to patterns used to fill polygon plots. To avoid overloading this meaning, I called it TickedStroke in Python.\nMatplotlib Example Carpet Plots Carpet plots are a common means of visualizing multi-dimensional data in certain fields such as aircraft design. These plots depict the response of a system of two independent variables plotted with a cheater axis.\nI developed some Matlab tools that make generating carpet plots easier. Routines for labeling the axes, placing text labels, and converting contour lines to the carpet plot axes are also included.\nMatlab File Exchange Contour Labels Positioning contour labels in Matlab is a hassle. Automatic placement is ugly and inconsistent while interactive placement is interactive and either painstaking or inconsistent.\nThis tool, clabel_along, allows the user to specify a curve along which to place contour labels. This gives the user a great deal of control for contour placement, but it also provides a system that is easily automated with repeatable results.\nGitHub Matlab File Exchange Text Labels Using MATLAB\u0026rsquo;s text to label points along a parametric curve often results in the label blocking the curve. This can be avoided for simple curves by using the text alignment properties or by offsetting the points. However, these techniques do not work for curves that change direction.\nThis tool, ptlabel_along, interpolates the provided curve to place points at just the desired parameter values. It also computes the local slope of the line and uses that to offset the text perpendicular to the line. This makes labeling parameter values along curves easy and beautiful.\nGitHub Matlab File Exchange ","permalink":"https://mcdonaldaerospace.com/projects/plotting/","summary":"Utilities to improve plotting and visualization.","title":"Plotting Tools"},{"content":"Late to the party (May of 2025), I took the plunge and got a Bambu P1S. It seemed like hobby grade 3D printers had matured such that they could be useful tools for making things instead of a novelty gadget to hack, wrench, and solder on. I had been burned by this promise a decade earlier, but costs had come down substantially ($800 vs $2500 and even lower now) and I wanted to believe. Fortunately, the promise held true and I\u0026rsquo;ve been having a lot more fun than I expected.\nSome people think that 3D printing is all hype, others will tell you it is the future of manufacturing, while others say it is only good for prototyping. There is truth to all of those points of view, but they\u0026rsquo;re also all wrong in other ways.\nFor me, the great thing about 3D printing is that it allows me to make things to solve niche problems in my life (or the lives of those around me). These are problems so specific that there is no viable market for someone to design, manufacture, and sell a product that solves the problem. 3D printing changes the economics of solving these problems in a profound way.\nI\u0026rsquo;ve become a bit evangelistic about 3D printing. I\u0026rsquo;ll keep it short: if you\u0026rsquo;re an engineer, you should have a 3D printer at home - having access to one at work doesn\u0026rsquo;t count.\nHere are some of the things I\u0026rsquo;ve designed and printed to solve problems in my life. Many of these are so hyper-specific that I can\u0026rsquo;t imagine that anyone else will ever need these files. So why share them? Well, it gives me joy and maybe it will inspire someone down the road to solve a problem in their life.\nBaking Prints My wife is an avid baker who seems to be the prime beneficiary of my 3D printing. Each year, she participates in the Great British Bake Off Bake Along - where home bakers attempt the technical challenge from the show each week. Between Bake Off and her other baking projects, there is an endless stream of things to be printed.\nBaking Sheet Rack Foot I purchased a rack for half sheet pans for my wife. It came with casters, but we didn\u0026rsquo;t want to use them in our setting. So I printed some feet for the extruded aluminum legs in TPU to protect the floor. Note that the flange is not equal on all four sides - this corresponds to some C-channel reinforcement around the legs where the casters bolted on.\n🍌 Downloads: STL | Fusion 360\nCustom Cookie Cutter I\u0026rsquo;ve heard the rule (paraphrased) that \u0026ldquo;If you have to do something a third time, you should make a tool\u0026rdquo;. This works for wood working, machining, software, etc.\nWell, lets just say that I\u0026rsquo;ve had to make more than three custom sized circle cookie cutters. I\u0026rsquo;ve often used OpenVSP because it makes the job easy. I finally decided to make a tool to make it even easier.\nOpenVSP has a Custom Component capability so users can write a script to make their own shapes with their own parameters. It is a great feature - that pretty much nobody ever uses. And I must admit, I\u0026rsquo;ve never used it myself - when I want a new feature in an OpenVSP component, I just add it to the C++ and then everybody gets the upgrade.\n🍌 Downloads: OpenVSP | OpenVSP Airshow\nDoughnut Cutter In Season 16, the \u0026lsquo;bread week\u0026rsquo; technical challenge was Doughnuts (are doughnuts really bread?). A stock biscuit cutter would have sufficed, but the ones in the drawer were not quite the right size (inch vs. metric), so I was asked to print a solution. I was leaning towards suggesting she make do with close enough when I realized that many of the contestants\u0026rsquo; doughnuts suffered from off-center holes that resulted in non-uniform doughnuts with uneven bakes. Clearly a custom doughnut cutter that would enforce concentricity was the solution.\n🍌 Downloads: STL | Fusion 360\nPlug Cutter Before I made the [Custom Cookie Cutter](projects/3Dprinting/Custom Cookie Cutter), GBBO had a recipe (which the contestants were not provided) that called for a 2cm hole to be cut 2.5cm into a bunch of little cakes. The void would later be filled with jam. She was worried about making the holes to the appropriate depth, so here is a a 2cm plug cutter with a 2.5cm built-in depth gauge.\n🍌 Downloads: STL | OpenVSP\nDough Divider My wife\u0026rsquo;s bagel game is on point. However, she found that portioning the dough into balls before shaping was tedious and error prone. Each ball had to be weighed and small bits cut off or added on until it was within tolerance. I had recently made her a butter press (on the mill, not 3D printed) from a Harbor Freight arbor press, so she asked if I could make her a dough divider for her arbor press. This works with an 8\u0026quot; cake pan. You press the dough into an even layer in the pan, give a quick press, and you get a dozen uniform portions for bagels, rolls, pretzels, breadsticks, etc.\n🍌 Downloads: STL | Fusion 360\nPie Stamps One Thanksgiving, my sister in law made both pumpkin and sweet potato pies with a top crust. She asked me to make these stamps to make sure the pies were marked to ensure everyone got the pie they wanted. Although I find both pumpkin and sweet potato objectionable, I was willing to help out.\n🍌 Downloads: STL\nRondo 503 Front Panel My wife has a Rondo 503 dough sheeter (Croissant anyone?). For the uninitiated, a dough sheeter is an industrial power tool version of a rolling pin. We got it used, with a busted up front panel that I set out to replace with a 3D print.\nAccording to FilamentColors, the best match for the Rondo is Gizmo Dorks orange PLA. It isn\u0026rsquo;t a perfect match, but it is pretty close.\nThis print is a bit tricky. You don\u0026rsquo;t want to print downward facing rounds, but the best orientation for the fillets causes most of the print to be an overhang. I solved this by designing my own support (instead of automatic support). Print the supports as solid objects with 5% infill and no top layers. Print the lid with solid infill as the orange filament is translucent enough that it doesn\u0026rsquo;t look good otherwise. This print will want to warp, but I was able to get it to stay flat using a high temperature plate and glue stick.\nNormal Exploded 🍌 Downloads: STL | Fusion 360\nHousehold and Kitchen Prints Headphone Hook My headphones chronically fall off my desk next to my computer. There is a whiteboard next to my seat that is mounted to the wall via standoffs. I threw together this print to give me a convenient place to put my headphones.\n🍌 Downloads: STL | Fusion 360\nKnife Block We recently purchased a new set of knives. This set came with an 11\u0026quot; carving knife. Unfortunately, our existing knife block could not accommodate an 11\u0026quot; knife - and it turns out that you can\u0026rsquo;t buy a knife block that will. So I designed this custom knife block to suit our set, including the 11\u0026quot; carver.\nThis prints in three pieces to avoid any overhangs and make efficient use of material. Ours is red and black. The Fusion files ended up a hot mess, so you only get the STL here. The base maxes out my 10\u0026quot; build volume in height and width. You\u0026rsquo;ll need to glue steel shot, rocks, or sand into the point of the base as a counterweight.\nNormal Exploded 🍌 Downloads: STL\nVIZIO Remote Soft Case In my household, the TV remote control (VIZIO XRT136) gets dropped. A lot. The back pops off, the batteries scatter, and after enough drops, the remote stops working and has to be replaced. You can buy protective cases for cell phones, but not for TV remotes.\nI actually designed this case (and the fixtures) in OpenVSP. It was a bit over the top, but I find Fusion\u0026rsquo;s controls for lofting and other organic 3D surfaces to be intolerable. Although modeling the shape of the remote itself in OpenVSP was relatively straightforward, tricking it into performing the Boolean operations required to form all the parts required some gymnastics that are not recommended. I\u0026rsquo;ve included the OpenVSP file, but if you want to print this, go straight to the STL.\nThe case prints in flexible TPU. Each half prints vertically to avoid needing supports. It is too tall and flexible to print in one piece this way, but I found that print quality was acceptable when split in two halves.\nThese halves must be bonded together. I solvent welded them using THF; this is nasty stuff, so be careful. I printed the fixtures in PLA to hold it all together through the process. I covered the fixtures in clear packing tape so they wouldn\u0026rsquo;t get glued to the case. I don\u0026rsquo;t know if it helped or not.\nNormal Exploded 🍌 Downloads: ZIP | OpenVSP\nDrawer Insert There is an awkward gap at the back of our kitchen drawer behind the silverware organizer. Space was wasted, things that fell back there were lost forever, and the organizer could slide around the drawer. I designed this insert to perfectly fill the gap and solve all these problems. There is a small radius on the interior corners to make removing small items easy. It is too big to print in one piece, so I split it in two and printed the halves vertically as towers.\nNormal Exploded 🍌 Downloads: STL | Fusion 360\nSpoon Tray One segment of our OXO silverware organizer was a catch all for unusual spoons. It held long iced tea spoons, tiny tea spoons, and sporks I made to match our silverware set. This led to total chaos. I designed this tray to fit perfectly in the OXO organizer and to bring order to the motley crew of spoons.\n🍌 Downloads: STL | Fusion 360\nFan Handle One benefit of living on the Central Coast of California is that we can keep our bedroom window open at night for most of the year. Sometimes on still nights, we place a cheap Lasko box fan in the window. Sometimes the box fan would fall out of the window with a clatter that would disturb, wake, and upset everyone (me, my wife, and the dog). If you manage to sleep through the fan crashing, you won\u0026rsquo;t sleep through the dog and the wife\u0026rsquo;s reactions.\nI designed this handle with a U-bracket to fit around the bottom of the window and keep the fan from falling out. The rest of the design was unnecessarily complex, but I wanted to go through the exercise of making the replacement handle match the factory handle as closely as possible - not just the dimensions and interface where it clips to the fan, but the overall shape, form and aesthetic. This prints in six pieces to avoid overhangs and so each piece prints in the best orientation for the strength considering the loads that will be on that part of the design. I assembled with super glue, but that was probably not necessary.\nNormal Exploded 🍌 Downloads: STL | Fusion 360\nPlastulette My friend Russ turned us on to the Servspoon, a small vintage stainless steel utensil that is super handy. Being stainless, it unfortunately isn\u0026rsquo;t compatible with some pots and pans. We wanted a nonstick safe version and 3D printing seemed the way to go. The Servspoon has a couple of bends in it. Rather than print this with the bends, I printed it flat and then droop-thermoformed it over a mold made from some scrap stainless sheet. I also milled a bevel into the leading edge. This was printed in PC to withstand dishwasher temperatures, but unfortunately it will not withstand cooking temperatures.\n🍌 Downloads: STL\nOther Prints Kia 2024 EV9 Key Fob Button We love our 2024 Kia EV9, but the remote key fob has a ton of buttons and lacks physical features that make it easy to register in your hand. In middle age, my lifelong myopia has been joined by presbyopia. Whenever I needed to lock or unlock the car, I found myself fumbling with the remote, taking off my glasses, and struggling to read the engraved icons on the buttons just inches from my face - almost always in the dark.\nI took apart the key fob and reverse engineered the lock button. I designed a replacement that is just a little taller, so it sits proud of the fob and provides registration in your hand. I can now lock and unlock the car effortlessly without even taking the key out of my pocket.\nI\u0026rsquo;ve had success printing this in PLA with a 0.4mm nozzle and standard layer heights. I tried building a lock icon into the face, but it was too small to print with the 0.4mm nozzle. When I get a 0.2mm nozzle, I will probably try again.\n🍌 Downloads: STL | Fusion 360\nApple Keyboard Stand When I replaced my old Apple keyboard, the new one no longer had a riser at the back setting the keys at a comfortable height and angle. This is a common problem and many similar stands exist on the 3D model sharing sites. I tried a few, but they each had problems. I combined design aspects of several to come up with one that works for me. It clips on and isn\u0026rsquo;t too tall or too short.\n🍌 Downloads: STL | Fusion 360\nTouchDRO Case I have a TouchDRO kit for my mill. I was one of the first to buy the new board and Yuri did not have a case available at the time. When I followed up later, the only case he had was for a later revision of the board. I made this case to match the style Yuri was providing at the time (laser cut plastic sheet). It has the advantage that all the pieces print flat, but it is a hassle to assemble and if I were doing it again, I would probably do it very differently.\nNormal Exploded 🍌 Downloads: STL | Fusion 360\nRIGID Shop Vac Adapter Long ago, the shop vac hose got chewed up by the dog. Sworn enemies, she saw her opportunity and she took it; I can\u0026rsquo;t really blame her. While you can buy replacement hoses and accessories, it didn\u0026rsquo;t seem cost effective to buy a $50 hose for a $100 vacuum - and I didn\u0026rsquo;t want to throw out an otherwise perfectly good tool. So for years, I shoved the hose and its accessories together with duct tape. It wasn\u0026rsquo;t pretty. There are many shop vac accessories on the 3D model sharing sites, but they all assume that the rest of your vacuum anatomy is intact. This is more of a prosthesis for the hose to restore the interface to all those accessories. Unsurprisingly, I designed this in OpenVSP\n🍌 Downloads: STL | OpenVSP\n","permalink":"https://mcdonaldaerospace.com/projects/3dprinting/","summary":"3D printable models and design files.","title":"3D Printing"},{"content":"Rob McDonald, Ph.D. I\u0026rsquo;m a freelance aerospace engineer working through McDonald Aerospace LLC, based in San Luis Obispo, California. My work sits at the intersection of aircraft design tools, advanced aircraft design, electric flight, computational methods, and open source software.\nWhat I Do My consulting activities focus on:\nConceptual aircraft design — rapid geometry, performance, and sizing methods to inform the early design process Electric flight and eVTOL design — flight physics for electric aircraft and advanced concept development for advanced air mobility Software and tool development — building pragmatic tools that help engineers do their job eVTOL market insight — help clients understand and navigate the eVTOL marketplace Background McDonald Aerospace LLC (2021 – present) Freelance consulting in advanced aircraft design, electric flight, and engineering software development.\nUber Elevate (2018 – 2021) Led the Technical Deep Dive team — although Uber was never going to develop our own aircraft, my team made sure we were a technically savvy customer. We set requirements, performed independent analysis of partner (and 3rd party) aircraft, conducted feasibility studies to push the art of the possible, investigated technologies to further the eVTOL ecosystem, and developed physics-based methods for evaluating electric propulsion, battery systems, acoustics, and vehicle performance.\nCal Poly San Luis Obispo (2006 – 2017) Professor of Aerospace Engineering - conducted research and taught aircraft design, performance, and multidisciplinary design optimization. Conducted more than $2.7M of sponsored research and secured more than $450k in donations supporting classes, clubs, and professional activity.\nOpen Source I am the primary developer and project lead of OpenVSP — a parametric aircraft geometry tool originally developed at NASA and now maintained as an open source project. OpenVSP has been widely adopted by established aerospace players as well as innovative startups across the Mach-altitude envelope.\nI created UnPlotter — a unique browser-based utility for extracting numerical data from figures in PDF files. If you have ever used conventional plot digitization tools, you will find that Unplotter is faster, easier, and far more accurate. A practical tool born from equal parts necessicity and obsessive attention to detail.\nI have developed and released several other small tools over the years, many are listed on the Aero Tools and Plotting pages of this site. All of them are available on GitHub.\nConnect GitHub LinkedIn ","permalink":"https://mcdonaldaerospace.com/about/","summary":"About Rob McDonald — aerospace engineer, software developer, and consultant.","title":"About"}]